Central Tendency
PSYC 2020-A01 / PSYC 6022-A01 | 2025-08-29 | Lab 2
Outline
- Assignment 1 Review
- Extra Credit
- R Projects
- Central Tendency Review
- R Functions
- Central Tendency in R
Learning objectives:
R: Projects, functions
Statistics: Central tendency
Housekeeping
Grading Display Modification
Moving from 0–100% to 10 points each
Top 10 lab assignments * 10 points each = 100%
Does not change anything about the weight!
RStudio
On lab computer
COS-GPU-2023
Assignment 1 Review
Check Working Directory
getwd()
Plotting
Make sure to select the right variable for plotting!
plot(iris$Sepal.Length, iris$Sepal.Width,
col = "#E50046")
plot(iris$Petal.Length, iris$Petal.Width,
col = "#C7DB9C")
R Projects
RStudio’s way of helping organizing files, scripts, etc.
I strongly recommend this!!
○ If you don’t already have a folder associated with this class, “New Directory”
○ If you do, “Existing Directory”
All R Scripts under the same project share a working directory
○ Location of files
○ Default folder for reading or writing files
Setting Working Directory
getwd() tells us the location of our working directory
setwd("C:/Users/Desktop/R Example") sets the working directory
Or, here::here() lets us do relative directories (my favorite!)
○ Just use the command at the top of the file to see where your directory is
○ Do need to install the here package first
Then, when you need a file, you can reference it relatively
[1] "C:/Users/jessi/OneDrive - Georgia Institute of Technology/Courses/GTA/PSYC 2020/PSYC 2020L Site"
here::here("lab 2", "cat.png")
[1] "C:/Users/jessi/OneDrive - Georgia Institute of Technology/Courses/GTA/PSYC 2020/PSYC 2020L Site/lab 2/cat.png"
Review of Central Tendency!
Mean: Sum of all values divided by the total number of values
Median: When sorted lowest to highest, the middle value
Mode: The value that appears most often
Central Tendency Practice
Given this dataset:
What is the mean? 2
What is the median? 2
What is the mode? 2
Central Tendency Practice
Given this dataset:
What is the mean? 1.5
What is the median? 1.5
What is the mode? No mode!
R Functions
A function performs some operation on an input and produces some output
Saw this last week
Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1 5.1 3.5 1.4 0.2 setosa
2 4.9 3.0 1.4 0.2 setosa
3 4.7 3.2 1.3 0.2 setosa
4 4.6 3.1 1.5 0.2 setosa
5 5.0 3.6 1.4 0.2 setosa
6 5.4 3.9 1.7 0.4 setosa
What is the function? Input? Output?
Central Tendency in R: Mean
We can calculate central tendencies in two ways:
Given this dataset, calculate the mean
With the
mean(x) function
○ x = vector of data
Central Tendency in R: Mode
Given this dataset, calculate the mode
With the mode() function
Doesn’t work :(
Have to create our own
R Functions
We’ve seen some built-in R functions (e.g., mean(), median()), but we can also make our own
function_name <- function(argument) {
do some stuff
return(this stuff)
}
ⓘ Don’t actually need to call return(); R will automatically return the last expression
Then, you can call the function
function_name(specific_argument)
To keep the results, make sure to assign them to some variable
very_important_results <- function_name(specific_argument)
R Functions
Let’s go back to finding the mode
Central Tendency in R: Mode
Given this dataset, calculate the mode
# note from jess: considering switching to just showing table()
c(2, 3, 12, 4, 4)
mode_func <- function(x) {
sort(table(x), decreasing = T)[1]
}
How does this work?
Descriptive Statistics in R
Takes time to look at all these for a lot of variables, even with functions
The summary(object) function provides us a quick overview of this information
○ object = for our purposes, a dataframe
What all do we get?
○ Minimum and maximum
○ 1st quantile, median, 3rd quantile
○ Mean
Visualizations!
Summary statistics are great, but don’t trust them alone!
What do you think a dataset with these descriptives would look like?
X_mean <- 54.26
Y_mean <- 47.83
X_sd <- 16.76
Y_sd <- 26.93
cor <- -0.06
Visualizations!
![]()
Visualizations
Don’t rush: graph your data!
What should graphs do?
○ Show the data
○ Draw the reader primarily to the data (not the graphical effects)
○ Avoid distorting the data
○ Present many numbers with minimum ink
○ Make large data sets coherent
○ Encourage the reader to compare different pieces of data
Visualizations: Histograms
An example of (simulated) SAT scores
What do we see here?
○ Outliers at zero! Not a possible SAT score
○ Negatively skewed: more data on the left than on the right
Skew
![]()
Positive skew, right-tailed
The mass of the distribution is concentrated on the left of the figure
Negative skew, left-tailed
The mass of the distribution is concentrated on the right of the figure
Skewness Demonstration
Full screen version here
Skewness demonstration!
Credits to Fabio Setti
Let’s Do Some Visualization
Base R Graphics
R has some plotting features built in—we saw this last week
plot(iris$Sepal.Length, iris$Sepal.Width)
What do we think about this?
Base R Graphics
Better… (thanks, ChatGPT)
plot(iris$Sepal.Length, iris$Sepal.Width,
pch = 19, # solid circles
col = "#377EB8", # pleasant blue
cex = 1.3, # slightly larger points
xlab = "Sepal Length", # cleaner label
ylab = "Sepal Width",
main = "Sepal Length vs Sepal Width",
cex.lab = 1.2, # bigger axis labels
cex.main = 1.4, # bigger title
font.main = 2) # bold title
We will learn a few plots in base R plotting, and then we will learn a better way of making plots: ggplot2
Let’s Do Some Visualization
Base R Graphics: Histogram
hist() function
Required arguments:
○ x = vector (variable) you want to plot (remember the $ function!)
Optional arguments:
○ breaks = bin count
○ main = title
○ xlab = label for x-axis
○ ylab = label for y-axis
○ col = color for bars
○ xlim = range for x-axis
○ ylim = range for y-axis
○ prob = T/F, proportion instead of frequency
If you do not set specific values for non-essential subarguments, it will use the default
hist(iris$Sepal.Length,
breaks = 7,
main = "Histogram of Sepal Length",
xlab = "Sepal Length",
xlim = c(3, 9),
border = "white",
col = "skyblue")
Let’s Do Some Visualization
Base R Graphics: Histogram
An important decision for histograms is this number (or width) of bins
Specified with the breaks argument
Let’s Do Some Visualization
Base R Graphics: Histogram
An important decision for histograms is this number (or width) of bins
Specified with the breaks argument
Let’s Do Some Visualization
Base R Graphics: Histogram
If we could make the bins infinitesimally small, we could get a probability density function (PDF)
dat <- data.frame(x = rnorm(1000))
cowplot::plot_grid(
plotlist = list(
ggplot(dat, aes(x = x)) +
geom_histogram(aes(y = after_stat(density)),
bins = 10) +
coord_cartesian(xlim = c(-4, 4), ylim = c(0, .5)) +
labs(y = "Proportion") +
cowplot::theme_cowplot(),
ggplot(dat, aes(x = x)) +
geom_histogram(aes(y = after_stat(density)),
bins = 50) +
coord_cartesian(xlim = c(-4, 4), ylim = c(0, .5)) +
labs(y = "Proportion") +
cowplot::theme_cowplot(),
ggplot(dat, aes(x = x)) +
geom_histogram(aes(y = after_stat(density)),
bins = 100) +
coord_cartesian(xlim = c(-4, 4), ylim = c(0, .5)) +
labs(y = "Proportion") +
cowplot::theme_cowplot(),
ggplot(dat, aes(x = x)) +
geom_histogram(aes(y = after_stat(density)),
bins = 100, alpha = .8) +
stat_function(inherit.aes = FALSE, fun = dnorm,
n = 101, args = list(mean = 0, sd = 1),
xlim = c(-4, 4),
color = "grey35", linewidth = 2) +
coord_cartesian(xlim = c(-4, 4), ylim = c(0, .5)) +
labs(y = "Proportion") +
cowplot::theme_cowplot()
),
nrow = 1)
Assignment 2
- Basic R functions
- Descriptive statistics
